That's a pretty weird "distance" unless you have some additional constraint like assuming the vectors are 2-norm normalised, in which case you get |a-b|^2 = 2(1-a.b).
It is natural to assume vectors have distance 0 from themselves at least, which this thing doesn't (in general). E.g. if you compute this "distance" for a = b = (2,0) then you get that the distance from a to itself is -3 which seems pretty weird.
It is natural to assume vectors have distance 0 from themselves at least, which this thing doesn't (in general). E.g. if you compute this "distance" for a = b = (2,0) then you get that the distance from a to itself is -3 which seems pretty weird.